Finite Group Databasebeta

← #20247008

Subgroups — #20247008

Order 6016.

952 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 952 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10625350C211yesmaximal, characteristic, complemented
2C2×#13094020C211yesmaximal, characteristic, complemented
3C2×#13094011C211yesmaximal, characteristic, complemented
4#15689031C214yesmaximal, complemented
5#15689028C211yesmaximal, characteristic, complemented
6#15689024C211yesmaximal, characteristic, complemented
7#15688999C214yesmaximal, complemented
8C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
9C2×#121×C47C211yesmaximal, characteristic, complemented
10C2×#10625350—24no—
11C2×#10625350—24no—
12C2×#10625350—24no—
13C22×Dic94C2211yescharacteristic
14C22×D188C2211yescharacteristic
15C22×C22⋊D47C2212yes—
16C22×C22⋊D47C2214yes—
17C22×C4×D47C2212yes—
18#13094020—24no—
19#13094011—24no—
20C2×C22⋊Dic47C2212yes—
21C2×C22⋊Dic47C2214yes—
22C2×(C2×D47)⋊C4C2214yes—
23C2×C4×Dic47C2211yescharacteristic
24C2×C4×Dic47C2211yescharacteristic
25C47⋊#95C2212yes—
26C47⋊#95C2214yes—
27C22×D4×C47C2211yescharacteristic
28C22×D4×C47C2212yes—
29C23×C4×C47C2211yescharacteristic
30#121×C47—24no—
31C2×C4⋊C4×C47C2211yescharacteristic
32C2×C22⋊C4×C47C2212yes—
33C24×C47C2312yes—
34C24×C47C2311yescharacteristic
35C23×D47C2312yes—
36C2×D4×C47—24no—
37C2×D4×C47—22no—
38C2×D4×C47—22no—
39C2×D4×C47—22no—
40C2×D4×C47—44no—
41C22×C4×C47—22no—
42C22×C4×C47—22no—
43C22×C4×C47D414yescomplemented
44C22×C4×C47C2312yes—
45C22×C4×C47C2311yescharacteristic
46C22×C4×C47C2311yescharacteristic
47C2×C22⋊D47—24no—
48C2×C22⋊D47—24no—
49C2×C22⋊D47—28no—
50C2×C22⋊D47—24no—
51C2×C22⋊D47—28no—
52C2×C22⋊D47—44no—
53C22×Dic47C2312yes—
54C22×Dic47C2312yes—
55C22×Dic47C2312yes—
56#10625350—232no—
57C2×D188—22no—
58C2×D188—22no—
59C2×D188D414yescomplemented
60C2×C4×D47—24no—
61C2×C4×D47—24no—
62C2×C4×D47—24no—
63C2×Dic94—22no—
64C2×Dic94—22no—
65C2×Dic94D414yescomplemented
66C4⋊C4×C47—22no—
67C22⋊C4×C47—24no—
68C22⋊Dic47—28no—
69C22⋊Dic47—24no—
70(C2×D47)⋊C4—44no—
71C4×Dic47—22no—
72C4×Dic47—22no—
73C23×C47—21no—
74C23×C47—21no—
75C23×C47—22no—
76C23×C47—22no—
77C23×C47—22no—
78C23×C47—22no—
79C23×C47—22no—
80C23×C47—24no—
81C23×C47—24no—
82C23×C47C2×D412yes—
83C23×C47C2411yescharacteristic
84C22×D47—22no—
85C22×D47—22no—
86C22×D47—24no—
87C22×D47—24no—
88C22×D47C2×D414yes—
89D4×C47—48no—
90D4×C47—44no—
91C2×C4×C47—21no—
92C2×C4×C47—21no—
93C2×C4×C47—28no—
94C2×C4×C47—22no—
95C2×C4×C47—24no—
96C2×C4×C47C2×D412yes—
97C2×C4×C47C2×D412yes—
98C2×C4×C47C2×D412yes—
99C2×C4×C47C2×D412yes—
100C22⋊D47—216no—
101C22⋊D47—416no—
102C2×Dic47—22no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47—22no—
106C2×Dic47—22no—
107C2×Dic47—22no—
108C2×Dic47—22no—
109C2×Dic47C2×D414yes—
110C2×Dic47#4114yescomplemented
111D188—28no—
112C4×D47—216no—
113Dic94—28no—
114C22×C47—22no—
115C22×C47—22no—
116C22×C47—22no—
117C22×C47—42no—
118C22×C47—42no—
119C22×C47—42no—
120C22×C47—42no—
121C22×C47—42no—
122C22×C47—44no—
123C22×C47—44no—
124C22×C47C22×D411yescharacteristic
125C22×C47C22×D411yescharacteristic
126C22×C47C22×D411yescharacteristic
127C22×C47C2×#4112yes—
128C22×C47H(5,𝔽2)12yes—
129C2×D47—24no—
130C2×D47—28no—
131C2×D47—42no—
132C2×D47—42no—
133C2×D47—44no—
134C4×C47—22no—
135C4×C47—42no—
136C4×C47#12014yes—
137Dic47—24no—
138Dic47—24no—
139Dic47—42no—
140#2431—471nomaximal, Sylow
141C2×C47—42no—
142C2×C47—82no—
143C2×C47C2×#12011yescharacteristic
144C2×C47#53211yescharacteristic
145C2×C47#53511yescharacteristic
146C2×C47#54612yes—
147C2×C47#55012yes—
148D47—44no—
149C22×#41—471no—
150C2×#127—471no—
151C2×#124—471no—
152C2×#121D4711yescharacteristic, complemented
153#392—474no—
154#391—471no—
155#390—471no—
156#386—474no—
157C4×C22⋊C4—471no—
158C47#243111yescharacteristic, complemented, Sylow
159C2×#41—944no—
160C2×#41—944no—
161C2×#41—944no—
162C22×Q8—471no—
163C22×D4—472no—
164C22×D4—474no—
165C22×D4—471no—
166C22×D4C2×D4711yescharacteristic
167C22×D4C2×D4712yes—
168C23×C4—472no—
169C23×C4C2×D4711yescharacteristic
170#127—944no—
171#124—944no—
172#121—24no—
173C2×C4⋊C4C2×D4711yescharacteristic
174C2×C22⋊C4—474no—
175C2×C22⋊C4—472no—
176C2×C22⋊C4—474no—
177C2×C22⋊C4C2×D4712yes—
178C2×C42—471no—
179C2×C42—471no—
180#95—472no—
181#95—474no—
182C24—472no—
183C24C22×D4712yes—
184C24C22×D4711yescharacteristic
185#41—9432no—
186C2×Q8—474no—
187C2×Q8—942no—
188C2×Q8—942no—
189C2×D4—24no—
190C2×D4—22no—
191C2×D4—22no—
192C2×D4—22no—
193C2×D4—44no—
194C2×D4—474no—
195C2×D4—944no—
196C2×D4—948no—
197C2×D4—944no—
198C2×D4—944no—
199C2×D4—948no—
200C2×D4—942no—
201C2×D4—942no—
202C2×D4—1884no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—472no—
206C22×C4—472no—
207C22×C4—472no—
208C22×C4—944no—
209C22×C4—944no—
210C22×C4—944no—
211C22×C4C22⋊D4714yescomplemented
212C22×C4C22×D4712yes—
213C22×C4C22×D4711yescharacteristic
214C22×C4C22×D4711yescharacteristic
215C4⋊C4—22no—
216C22⋊C4—24no—
217C22⋊C4—944no—
218C22⋊C4—948no—
219C22⋊C4—1884no—
220C42—942no—
221C42—942no—
222C23—21no—
223C23—21no—
224C23—22no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—24no—
230C23—24no—
231C23—474no—
232C23—942no—
233C23—942no—
234C23—944no—
235C23—944no—
236C23C2×C22⋊D4712yes—
237C23C23×D4711yescharacteristic
238Q8—948no—
239D4—48no—
240D4—44no—
241D4—9416no—
242D4—948no—
243D4—18816no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—28no—
247C2×C4—22no—
248C2×C4—24no—
249C2×C4—474no—
250C2×C4—474no—
251C2×C4—9416no—
252C2×C4—942no—
253C2×C4—942no—
254C2×C4—942no—
255C2×C4—942no—
256C2×C4—942no—
257C2×C4—942no—
258C2×C4—942no—
259C2×C4D4×D4712yes—
260C2×C4D4×D4712yes—
261C2×C4C2×C22⋊D4712yes—
262C2×C4C2×C22⋊D4712yes—
263C22—22no—
264C22—22no—
265C22—22no—
266C22—42no—
267C22—42no—
268C22—44no—
269C22—44no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22—948no—
274C22—944no—
275C22—1884no—
276C22—1882no—
277C22—1882no—
278C22C2×D4×D4711yescharacteristic
279C22C2×D4×D4711yescharacteristic
280C22C22×C22⋊D4711yescharacteristic
281C22#41×D4712yes—
282C22#1309406912yes—
283C4—22no—
284C4—42no—
285C4—944no—
286C4—944no—
287C4—1882no—
288C4#1309399214yes—
289C2—42no—
290C2—82no—
291C2—1884no—
292C2C2×#1309399211yescharacteristic
293C2#1568966911yescharacteristic
294C2#1568969011yescharacteristic
295C2#1568977012yes—
296C2#1568979112yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#121×C47C2
hypercenterC2×#121D47
hypocenterC47#2431
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#121

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#10625350C2semidirect
2. C2×#13094020C2semidirect
3. C2×#13094011C2semidirect
4. #15689031C2semidirect
5. #15689028C2semidirect
6. #15689024C2semidirect
7. #15688999C2semidirect
8. C4×C22⋊Dic47C2semidirect
9. C2×#121×C47C2semidirect
43. C22×C4×C47D4semidirect
59. C2×D188D4semidirect
65. C2×Dic94D4semidirect
110. C2×Dic47#41semidirect
152. C2×#121D47semidirect
158. C47#2431semidirect
211. C22×C4C22⋊D47semidirect